Here's a few random leader ideas I have, with no regard for how likely they are or precedent with which civs get alternatives, or the fact that half (at least!) of these are jokes...
USA: Eisenhower. Ability: Once railroads are introduced, trade routes automatically make railroads behind them *while in your own lands*. (assuming you have the iron/coal). Cities connected to the capital by railroad gain +25% gold and +10% production. (Let's pretend the railraods are the highway system Eisenhower introduced).
Australia: Harold Holt. Builders gain +2 charges the first time they embark, but have a 25% chance to drown each turn they're embarked. (too soon?)
Egypt: Akhenaten. When you "earn" a dark age, you can choose a new religious belief to add on to your religion (old things are not replaced). -2 loyalty in each of your own cities for every religious tenant in that city's majority religion. Both of these remain for the rest of the game. Keep sabotaging yourself and get a mega-religion for later, if you can handle your people...
Greece: Diogenes. Unique neighborhood replacement: Barrel. Arrives at construction. Only gives 2 housing and -1 appeal, but gives 2 amenities, and an adjacency bonus from adjacent districts (culture from acropolis, science from campus, etc). Immune from recruit partisans, becuase spies don't want to go near it.
Maya: Targitzan. When founding each city, one source of stone randomly appears within working radius, and one more appears for each government plaza building (just in that city). 25% chance that it's marble or jade instead. Gains the unique tile improvement, dart shooting statue. Can only be built on jade or any quarryable resource (side note, Jade really should be quarried, not mined in the based game...). +1 faith and +1 production. Nearest enemy unit, within 3 tiles, loses 50 HP each turn unless the improvement is pillaged (pillaging it gives extra yields).
Phoeniecia: Hannibal. Gains the unique unit, elephant cavalry. Replaces heavy chariot. Doesn't require horses, but requires you have at least one source of ivory (which he has a start bias for, don't worry!). -1 move, no rough terrain penalty, attacks cities/walls for full damage. All units within effect range (regardless of era) can walk over mountains, but lose 50 HP if you end your turn in one (like in civ 5... so you can't snipe from mountains with ranged units that can't get attacked!). Yeah I basically stole this from civ 5.
Rome: Commodus. +50% production to entertainment complexes/water parks and their buildings. Gains unique civillian unit, himself. Only one can exist at a time. When stationed on an entertainment complex/water park, its amenities and the tourism and yields of its buildings, and any adjacent wonders, are doubled (if it's yours) and all your units within 2 tiles gain +25% strength (no matter who's the district is). When killed, teleports back to the capital, like a great general. Roman forts within your territory give +1 culture and faith. (For flavor, Trajan's Roman Forts now give +1 production and gold when in your territory).
Rome again: Nero. +5 great music slots in the capital, and for each one filled, units born in the capital gain +5% combat strength. Gain great musician points when you raze a city.